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Dilogarithm functional equations: FullSimplify & FunctionExpand

Posted 16 days ago
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I am a new Mathematica user. Performing some integration, I get a number of terms that involve the dilogarithm function. However, Mathematica does not seem to recognize functional equation relationships that would simplify things considerable. A simple example of a term that is not simplified would be

PolyLog[2,E^d/(1+E^d)]+ PolyLog[2,1/(1+E^d)]

In this case, neither FullSimplify or FunctionExpand will give the simpler result in terms of logarithms (they return the form as above).

However, suppose that I had the equivalent statement

PolyLog[2,E^d/(1+E^d)]+ PolyLog[2,1 - E^d/(1+E^d)]

In this case, FunctionExpand now gives the expected result in terms of logarithms. That is

\[Pi]^2/6-Log[E^d/(1+E^d)] Log[1-E^d/(1+E^d)] 

whereas FullSimplify does not. Is this expected behavior? Is there a way to make Mathematica recognize the functional relationships without rewriting things?

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